28edo: Difference between revisions

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~~'''28 equal divisions of the octave''' ('''28edo''') is the [[tuning system]] derived by dividing the [[octave]] into 28 equal steps of approximately 42.857~~{{~~cent~~}} ~~each.~~

== Theory ==

28edo is a multiple of both [[7edo]] and [[14edo]] (and of course [[2edo]] and [[4edo]]). It shares three intervals with [[12edo]]: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it [[tempering_out|tempers out]] the [[greater diesis]] [[648/~~625|648:~~625]]. It does not however temper out the [[128/~~125|128:~~125]] [[lesser_diesis|lesser diesis]], as 28 is not divisible by 3. It has the same perfect fourth and fifth as 7edo. It also has decent approximations of several septimal intervals, of which [[9/7]] and its inversion [[14/9]] are also found in 14edo. Its approximation to [[5/4]] is unusually good for an edo of this size, being the next convergent to log25 after [[3edo]].

28edo is a multiple of both [[7edo]] and [[14edo]] (and of course [[2edo]] and [[4edo]]). It shares three intervals with [[12edo]]: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it [[tempering_out|tempers out]] the [[greater diesis]] [[648/625]]. It does not however temper out the [[128/125]] [[lesser_diesis|lesser diesis]], as 28 is not divisible by 3. It has the same perfect fourth and fifth as 7edo. It also has decent approximations of several septimal intervals, of which [[9/7]] and its inversion [[14/9]] are also found in 14edo. Its approximation to [[5/4]] is unusually good for an edo of this size, being the next convergent to log25 after [[3edo]].

28edo can approximate the [[7-limit|7-limit]] subgroup 2.27.5.21 quite well, and on this subgroup it has the same commas and tunings as 84edo. The temperament corresponding to [[Semicomma_family|orwell temperament]] now has a major third as generator, though as before 225/224, 1728/1715 and 6144/6125 are tempered out. The 225/224-tempered version of the [[Marvel_chords|augmented triad]] has a very low complexity, so many of them appear in the [[MOS scales]] for this temperament, which have sizes 7, 10, 13, 16, 19, 22, 25.

Line 22:

! colspan="2" | Just (j)

! rowspan="2" | Delta (e-j)

! rowspan="2" colspan="3" | [[Ups and ~~Downs Notation~~]]

! rowspan="2" colspan="3" | [[Ups and downs notation]]

|-

! Cents

Line 290:

|}

== Chord ~~Names~~ ==

== Notation ==

=== Ups and downs notation ===

As 28edo tempers out the [[2187/2048|Pythagorean apotome]], the traditional sharps and flats have no effect on the pitch. Therefore, with [[ups and downs notation]], arrows are required.

=== Sagittal notation ===

This notation uses the same sagittal sequence as EDOs [[23edo#Sagittal notation|23]] and [[33edo#Sagittal notation|33]], and is a superset of the notations for EDOs [[14edo#Sagittal notation|14]] and [[7edo#Sagittal notation|7]].

File:28-EDO_Sagittal.svg

desc none

rect 80 0 300 50 [[Sagittal_notation]]

rect 447 0 607 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]

rect 20 80 447 106 [[Fractional_3-limit_notation#Bad-fifths_limma-fraction_notation | limma-fraction notation]]

default [[File:28-EDO_Sagittal.svg]]

</imagemap>

== Chord names ==

Ups and downs can be used to name 28edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used.

Line 303:

Line 320:

* 0-7-16-23 = C vE G vB = Cv7 = C down-seven

For a more complete list, see [[Ups and ~~Downs Notation~~ #Chord names in other EDOs]].

For a more complete list, see [[Ups and downs notation #Chord names in other EDOs]].

== Rank ~~two~~ temperaments ==

== Regular temperament properties ==

=== Rank-2 temperaments ===

{| class="wikitable center-1 center-2"

|-

! Periods per ~~octave~~

! Periods per 8ve

! Generator

! Temperaments

Line 330:

Line 348:

| 1

| 11\28

| [[~~Oneirotonic~~]]

| [[A-team]]

|-

| 1

Line 342:

Line 360:

| 2

| 3\28

| [[~~Trienstonic_clan#Octokaidecal|~~Octokaidecal]]

| [[Octokaidecal]]

|-

| 2

Line 369:

Line 387:

|}

== Commas ==

=== Commas ===

~~28 EDO~~ [[tempers out]] the following [[comma]]s. ~~(Note:~~ This assumes the [[val]] {{val| 28 44 65 79 97 104 }}.)

28et [[tempering out|tempers out]] the following [[comma]]s. This assumes the [[val]] {{val| 28 44 65 79 97 104 }}.

{| class="commatable wikitable center-all left-3 right-4 left-6"

|-

! [[Harmonic Limit|Prime ~~Limit~~]]

! [[Harmonic Limit|Prime limit]]

! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>

! [[Monzo]]

Line 393:

Line 411:

| 62.57

| Quadgu

| ~~Major~~ diesis~~, diminished comma~~

| Diminished comma, major diesis

|-

| 5

Line 414:

Line 432:

| 48.77

| Rugu

| ~~Septimal~~ quartertone

| Mint comma, septimal quartertone

|-

| 7

Line 421:

Line 439:

| 34.98

| Biruyo

| ~~Tritonic~~ diesis~~, Jubilisma~~

| Jubilisma, tritonic diesis

|-

| 7

Line 428:

Line 446:

| 21.18

| Triru-aquinyo

| Gariboh

| Gariboh comma

|-

| 7

Line 435:

Line 453:

| 13.79

| Zotrigu

| ~~Septimal semicomma,~~ Starling comma

| Starling comma, septimal semicomma

|-

| 7

Line 442:

Line 460:

| 2.35

| Lazoquinyo

| Horwell

| Horwell comma

|-

| 7

Line 449:

Line 467:

| 0.34

| Trisa-seprugu

| [[Akjaysma]]~~, 5\7-octave comma~~

| [[Akjaysma]]

|-

| 11

Line 470:

Line 488:

| 3.03

| Triluyo

| Wizardharry

| Wizardharry comma

|}

== Octave stretch or compression ==

'''[[equal tuning |89ed9]]''', a [[octave shrinking|compressed-octaves]] tuning of 28edo, makes 28edo potentially useable as a [[dual-fifth]] tuning. It shares the error equally between 28edo's two perfect fifths.

So, where pure-octaves 28edo has a flat fifth with 16.2{{c}} error and a sharp fifth with 28.6{{c}} error, 89ed9 instead has a flat fifth with 21.4{{c}} error and a sharp fifth with 21.4{{c}} error.

21.4{{c}} error is slightly better than [[23edo]]'s best fifth but slightly worse than [[5edo]]'s.

Some might consider this fifth too bad to use, in which case 89ed9 would be a downgrade from pure-octaves 28edo.

Others might consider it just useable enough, in which case 89ed9 would be an upgrade because it has one more useable interval and one less [[wolf interval]].

89ed9 approximates the no-3s 7-, 11-, 13-, 17-, 19- and 23-limits significantly better than pure-octaves 28edo.

; 28edo

* Step size: 42.8571{{c}}, octave size: 1200.00{{c}}

Approximates all no-3s harmonics up to 7 within ''16.9''{{c}}.

Approximates all no-3s harmonics up to 11 & up to 13 within ''16.9''{{c}}.

Approximates all no-3s harmonics up to 17 & up to 19 within ''19.2''{{c}}.

{{Harmonics in equal|28|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 28edo}}

{{Harmonics in equal|28|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 28edo (continued)}}

; [[equal tuning|89ed9]]

* Step size: 42.7406{{c}}, octave size: 1196.74{{c}}

Approximates all no-3s harmonics up to 7 within ''8.2''{{c}}.

Approximates all no-3s harmonics up to 11 & up to 13 within ''11.4''{{c}}.

Approximates all no-3s harmonics up to 17 & up to 19 within ''11.4''{{c}}.

{{Harmonics in equal|89|9|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 89ed9}}

{{Harmonics in equal|89|9|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 89ed9 (continued)}}

== Scales ==

28edo is particularly well suited to Whitewood in the same way that [[15edo|15edo]] is for Blackwood, as it has one third that is heavily tempered, but in a familiar way shared with 12edo, while the other one is significantly closer to just. (Contrast with 20 & 21edo, where one third remains the same as in 12, and the other is pushed further away, making the overall sound considerably more xenharmonic) This makes the 5ths more out of tune, but in a useful way, as you can stack major and minor thirds indefinitely until they repeat 4 octaves and 14 notes up, producing one of the largest nonrepeating harmonious chords possible in an edo this low. This produces mode of symmetry scales with two different modes and 4 different keys, making it equally easy to establish any chord in the scale as the root and modulate between them.

; Whitewood scales

28edo is particularly well suited to [[Whitewood]] in the same way that [[15edo|15edo]] is for [[Blackwood]], as it has one third that is heavily tempered, but in a familiar way shared with 12edo, while the other one is significantly closer to just. (Contrast with 20 & 21edo, where one third remains the same as in 12, and the other is pushed further away, making the overall sound considerably more xenharmonic). This makes the 5ths more out of tune, but in a useful way, as you can stack major and minor thirds indefinitely until they repeat 4 octaves and 14 notes up, producing one of the largest nonrepeating harmonious chords possible in an edo this low. This produces mode of symmetry scales with two different modes and 4 different keys, making it equally easy to establish any chord in the scale as the root and modulate between them.

* Whitewood Major [14] 13131313131313

Line 484:

Line 536:

* (Whitewood neutral is also theoretically possible, stacking neutral or subminor & supermajor thirds, but in practice that works out as 22222222222222, or 14edo, so it doesn't count as a 28edo scale)

; Negri scales

If you're looking for something a little more xenharmonic sounding, but still relatively low in badness, Negri [9] & [10] function very similarly to Porcupine [7] & [8] in 15edo, further cementing the idea that 28 is to 15 what 29 is to 12 - a similar structure, but with tempering errors in the opposite direction and slightly greater complexity. Both have a decent selection of familiar major and minor chords clustered towards one end of the scale, while the way they modulate between one-another and the melodies they form is quite alien to people used to the diatonic scale. Most of the compositional notes on the Porcupine page can also be applied here.

Line 490:

Line 543:

* Negri [19] 2121212121212121211

; Diatonic scales

However, unlike 15, 28 is complex enough to do recognisable approximations of various diatonic scales and their modes, although they will sound noticeably out of tune and it's obviously not the best method of using the temperament.

Line 525:

Line 579:

* Melodic Major [16] 2122221222122212

; Oneirotonic scales

Interestingly, as it has a near perfect 21/16, 28edo can also generate Oneirotonic scales (see [[13edo|13edo]]) by stacking it's 11th degree, and they actually sound better in this temperament.

Line 536:

Line 591:

* [[machine11]]

* [[machine17]]

; Other Scales

* 10-tone 4&7edo scale 4 3 1 4 2 2 4 1 3 4

== Instruments ==

28edo can be played on the [[Lumatone]]. See [[Lumatone mapping for 28edo]].

28edo can also be played on a [[14edo]] [[guitar]] with very little effort. See [[User:MisterShafXen/Skip fretting system 28 2 3]].

== Music ==

; Ambient Esoterica

; [[Ambient Esoterica]]

* [https://www.youtube.com/watch?v=d_55LCULX9g ''28 Mansions of the Moon'']

; Beheld

; [[Beheld]]

* [https://www.youtube.com/watch?v=0nvrUbw1VLQ ''Haze vibe'']

; duckapus

; [[Bryan Deister]]

* [https://www.youtube.com/shorts/1nWL2qEcI-Q ''28edo improvisation''] (2022)

* [https://www.youtube.com/shorts/sCE0MjUyRUk ''28edo blues''] (2023)

* [https://www.youtube.com/shorts/--BIQKJ9uvI ''minuet in 28edo''] (2025)

* [https://www.youtube.com/shorts/vEcihDrmddg ''Fantasy in 28edo''] (2026)

; [[duckapus]]

* [https://www.youtube.com/watch?v=F74B9qUpYi8 ''G.27 Variations in 28edo''] (2023)

; [[User:Eliora|Eliora]]

* [https://www.youtube.com/watch?v=ghVCGlm7yOk ''Fantasy for Piano'']

* [https://www.youtube.com/watch?v=ghVCGlm7yOk ''Fantasy for Piano (and strings)''] (2021)

; Kosmorksy

; [[Francium]]

* [https://www.youtube.com/watch?v=8dubV7STjJA ''According to a Tomato''] (2025)

; [[Kosmorksy]]

* [https://www.youtube.com/watch?v=26UpCbrb3mE ''28 tone Prelude'']

; [[Claudi Meneghin]]

; [[User:Phanomium|Phanomium]]

* ''[https://www.youtube.com/watch?v=zZJ5b4SkT7Q Euxenite]'' (2025)

;[[Claudi Meneghin]]

* [https://www.youtube.com/watch?v=30XUKJsaINU ''Happy Birthday Canon'', 5-in-1 Canon in 28edo]

* [https://www.youtube.com/watch?v=wYdRAzp8Qi0 ''Canon on Twinkle Twinkle Little Star'', for Baroque Oboe & Viola] (2023) – ([https://www.youtube.com/watch?v=B1KZoLR8UTI for Organ])

; [[NullPointerException Music]]

* [https://www.youtube.com/watch?v=vw6l5b3oGk0 ''Edolian - Machinery''] (2020)

; [[User:Userminusone|Userminusone]]

* [https://youtu.be/NbR3i45qQVQ ''Purple Skyes'']

~~[[Category:28edo| ]] ~~

~~[[Category:Equal divisions of the octave|##]] ~~

[[Category:Twentuning]]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''28 equal divisions of the octave''' ('''28edo''') is the [[tuning system]] derived by dividing the [[octave]] into 28 equal steps of approximately 42.857{{cent}} each.
+{{ED intro}}
 == Theory ==
 {{Harmonics in equal|28}}
+{{Harmonics in equal|28|start=12|collapsed=1|intervals=odd}}
-edo is a multiple of both [[7edo]] and [[14edo]] (and of course [[2edo]] and [[4edo]]). It shares three intervals with [[12edo]]: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it [[tempering_out|tempers out]] the [[greater diesis]] [[648/625|648:625]]. It does not however temper out the [[128/125|128:125]] [[lesser_diesis|lesser diesis]], as 28 is not divisible by 3. It has the same perfect fourth and fifth as 7edo. It also has decent approximations of several septimal intervals, of which [[9/7]] and its inversion [[14/9]] are also found in 14edo. Its approximation to [[5/4]] is unusually good for an edo of this size, being the next convergent to log<sub>2</sub>5 after [[3edo]].
+edo is a multiple of both [[7edo]] and [[14edo]] (and of course [[2edo]] and [[4edo]]). It shares three intervals with [[12edo]]: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it [[tempering_out|tempers out]] the [[greater diesis]] [[648/625]]. It does not however temper out the [[128/125]] [[lesser_diesis|lesser diesis]], as 28 is not divisible by 3. It has the same perfect fourth and fifth as 7edo. It also has decent approximations of several septimal intervals, of which [[9/7]] and its inversion [[14/9]] are also found in 14edo. Its approximation to [[5/4]] is unusually good for an edo of this size, being the next convergent to log<sub>2</sub>5 after [[3edo]].
 edo can approximate the [[7-limit|7-limit]] subgroup 2.27.5.21 quite well, and on this subgroup it has the same commas and tunings as 84edo. The temperament corresponding to [[Semicomma_family|orwell temperament]] now has a major third as generator, though as before 225/224, 1728/1715 and 6144/6125 are tempered out. The 225/224-tempered version of the [[Marvel_chords|augmented triad]] has a very low complexity, so many of them appear in the [[MOS scales]] for this temperament, which have sizes 7, 10, 13, 16, 19, 22, 25.
@@ Line 22: / Line 22: @@
 ! colspan="2" | Just (j)
 ! rowspan="2" | Delta <br> (e-j)
-! rowspan="2" colspan="3" | [[Ups and Downs Notation]]
+! rowspan="2" colspan="3" | [[Ups and downs notation]]
 |-
 ! Cents
@@ Line 290: / Line 290: @@
 |}
-== Chord Names ==
+== Notation ==
+=== Ups and downs notation ===
+As 28edo tempers out the [[2187/2048|Pythagorean apotome]], the traditional sharps and flats have no effect on the pitch. Therefore, with [[ups and downs notation]], arrows are required.
+{{ups and downs sharpness}}
+=== Sagittal notation ===
+This notation uses the same sagittal sequence as EDOs [[23edo#Sagittal notation|23]] and [[33edo#Sagittal notation|33]], and is a superset of the notations for EDOs [[14edo#Sagittal notation|14]] and [[7edo#Sagittal notation|7]].
+<imagemap>
+File:28-EDO_Sagittal.svg
+desc none
+rect 80 0 300 50 [[Sagittal_notation]]
+rect 447 0 607 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
+rect 20 80 447 106 [[Fractional_3-limit_notation#Bad-fifths_limma-fraction_notation | limma-fraction notation]]
+default [[File:28-EDO_Sagittal.svg]]
+</imagemap>
+== Chord names ==
 Ups and downs can be used to name 28edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used.
@@ Line 303: / Line 320: @@
 * 0-7-16-23 = C vE G vB = Cv7 = C down-seven
-For a more complete list, see [[Ups and Downs Notation #Chord names in other EDOs]].
+For a more complete list, see [[Ups and downs notation #Chord names in other EDOs]].
-== Rank two temperaments ==
+== Regular temperament properties ==
+=== Rank-2 temperaments ===
 {| class="wikitable center-1 center-2"
 |-
-! Periods <br> per octave
+! Periods<br>per 8ve
 ! Generator
 ! Temperaments
@@ Line 330: / Line 348: @@
 | 1
 | 11\28
-| [[Oneirotonic]]
+| [[A-team]]
 |-
 | 1
@@ Line 342: / Line 360: @@
 | 2
 | 3\28
-| [[Trienstonic_clan#Octokaidecal|Octokaidecal]]
+| [[Octokaidecal]]
 |-
 | 2
@@ Line 369: / Line 387: @@
 |}
-== Commas ==
+=== Commas ===
-EDO [[tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 28 44 65 79 97 104 }}.)
+et [[tempering out|tempers out]] the following [[comma]]s. This assumes the [[val]] {{val| 28 44 65 79 97 104 }}.
 {| class="commatable wikitable center-all left-3 right-4 left-6"
 |-
-! [[Harmonic Limit|Prime<br>Limit]]
+! [[Harmonic Limit|Prime<br>limit]]
 ! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
 ! [[Monzo]]
@@ Line 393: / Line 411: @@
 | 62.57
 | Quadgu
-| Major diesis, diminished comma
+| Diminished comma, major diesis
 |-
 | 5
@@ Line 414: / Line 432: @@
 | 48.77
 | Rugu
-| Septimal quartertone
+| Mint comma, septimal quartertone
 |-
 | 7
@@ Line 421: / Line 439: @@
 | 34.98
 | Biruyo
-| Tritonic diesis, Jubilisma
+| Jubilisma, tritonic diesis
 |-
 | 7
@@ Line 428: / Line 446: @@
 | 21.18
 | Triru-aquinyo
-| Gariboh
+| Gariboh comma
 |-
 | 7
@@ Line 435: / Line 453: @@
 | 13.79
 | Zotrigu
-| Septimal semicomma, Starling comma
+| Starling comma, septimal semicomma
 |-
 | 7
@@ Line 442: / Line 460: @@
 | 2.35
 | Lazoquinyo
-| Horwell
+| Horwell comma
 |-
 | 7
@@ Line 449: / Line 467: @@
 | 0.34
 | Trisa-seprugu
-| [[Akjaysma]], 5\7-octave comma
+| [[Akjaysma]]
 |-
 | 11
@@ Line 470: / Line 488: @@
 | 3.03
 | Triluyo
-| Wizardharry
+| Wizardharry comma
 |}
 <references/>
+== Octave stretch or compression ==
+'''[[equal tuning |89ed9]]''', a [[octave shrinking|compressed-octaves]] tuning of 28edo, makes 28edo potentially useable as a [[dual-fifth]] tuning. It shares the error equally between 28edo's two perfect fifths.
+So, where pure-octaves 28edo has a flat fifth with 16.2{{c}} error and a sharp fifth with 28.6{{c}} error, 89ed9 instead has a flat fifth with 21.4{{c}} error and a sharp fifth with 21.4{{c}} error.
+.4{{c}} error is slightly better than [[23edo]]'s best fifth but slightly worse than [[5edo]]'s.
+Some might consider this fifth too bad to use, in which case 89ed9 would be a downgrade from pure-octaves 28edo.
+Others might consider it just useable enough, in which case 89ed9 would be an upgrade because it has one more useable interval and one less [[wolf interval]].
+ed9 approximates the no-3s 7-, 11-, 13-, 17-, 19- and 23-limits significantly better than pure-octaves 28edo.
+; 28edo
+* Step size: 42.8571{{c}}, octave size: 1200.00{{c}}
+Approximates all no-3s harmonics up to 7 within ''16.9''{{c}}.
+Approximates all no-3s harmonics up to 11 & up to 13 within ''16.9''{{c}}.
+Approximates all no-3s harmonics up to 17 & up to 19 within ''19.2''{{c}}.
+{{Harmonics in equal|28|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 28edo}}
+{{Harmonics in equal|28|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 28edo (continued)}}
+; [[equal tuning|89ed9]]
+* Step size: 42.7406{{c}}, octave size: 1196.74{{c}}
+Approximates all no-3s harmonics up to 7 within ''8.2''{{c}}.
+Approximates all no-3s harmonics up to 11 & up to 13 within ''11.4''{{c}}.
+Approximates all no-3s harmonics up to 17 & up to 19 within ''11.4''{{c}}.
+{{Harmonics in equal|89|9|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 89ed9}}
+{{Harmonics in equal|89|9|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 89ed9 (continued)}}
 == Scales ==
-edo is particularly well suited to Whitewood in the same way that [[15edo|15edo]] is for Blackwood, as it has one third that is heavily tempered, but in a familiar way shared with 12edo, while the other one is significantly closer to just. (Contrast with 20 & 21edo, where one third remains the same as in 12, and the other is pushed further away, making the overall sound considerably more xenharmonic) This makes the 5ths more out of tune, but in a useful way, as you can stack major and minor thirds indefinitely until they repeat 4 octaves and 14 notes up, producing one of the largest nonrepeating harmonious chords possible in an edo this low. This produces mode of symmetry scales with two different modes and 4 different keys, making it equally easy to establish any chord in the scale as the root and modulate between them.
+; Whitewood scales
+edo is particularly well suited to [[Whitewood]] in the same way that [[15edo|15edo]] is for [[Blackwood]], as it has one third that is heavily tempered, but in a familiar way shared with 12edo, while the other one is significantly closer to just. (Contrast with 20 & 21edo, where one third remains the same as in 12, and the other is pushed further away, making the overall sound considerably more xenharmonic). This makes the 5ths more out of tune, but in a useful way, as you can stack major and minor thirds indefinitely until they repeat 4 octaves and 14 notes up, producing one of the largest nonrepeating harmonious chords possible in an edo this low. This produces mode of symmetry scales with two different modes and 4 different keys, making it equally easy to establish any chord in the scale as the root and modulate between them.
 * Whitewood Major [14] 13131313131313
@@ Line 484: / Line 536: @@
 * (Whitewood neutral is also theoretically possible, stacking neutral or subminor & supermajor thirds, but in practice that works out as 22222222222222, or 14edo, so it doesn't count as a 28edo scale)
+; Negri scales
 If you're looking for something a little more xenharmonic sounding, but still relatively low in badness, Negri [9] & [10] function very similarly to Porcupine [7] & [8] in 15edo, further cementing the idea that 28 is to 15 what 29 is to 12 - a similar structure, but with tempering errors in the opposite direction and slightly greater complexity. Both have a decent selection of familiar major and minor chords clustered towards one end of the scale, while the way they modulate between one-another and the melodies they form is quite alien to people used to the diatonic scale. Most of the compositional notes on the Porcupine page can also be applied here.
@@ Line 490: / Line 543: @@
 * Negri [19] 2121212121212121211
+; Diatonic scales
 However, unlike 15, 28 is complex enough to do recognisable approximations of various diatonic scales and their modes, although they will sound noticeably out of tune and it's obviously not the best method of using the temperament.
@@ Line 525: / Line 579: @@
 * Melodic Major [16] 2122221222122212
+; Oneirotonic scales
 Interestingly, as it has a near perfect 21/16, 28edo can also generate Oneirotonic scales (see [[13edo|13edo]]) by stacking it's 11th degree, and they actually sound better in this temperament.
@@ Line 536: / Line 591: @@
 * [[machine11]]
 * [[machine17]]
+; Other Scales
+* 10-tone 4&7edo scale 4 3 1 4 2 2 4 1 3 4
+== Instruments ==
+edo can be played on the [[Lumatone]]. See [[Lumatone mapping for 28edo]].
+edo can also be played on a [[14edo]] [[guitar]] with very little effort. See [[User:MisterShafXen/Skip fretting system 28 2 3]].
 == Music ==
-; Ambient Esoterica
+; [[Ambient Esoterica]]
 * [https://www.youtube.com/watch?v=d_55LCULX9g ''28 Mansions of the Moon'']
-; Beheld
+; [[Beheld]]
 * [https://www.youtube.com/watch?v=0nvrUbw1VLQ ''Haze vibe'']
-; duckapus
+; [[Bryan Deister]]
+* [https://www.youtube.com/shorts/1nWL2qEcI-Q ''28edo improvisation''] (2022)
+* [https://www.youtube.com/shorts/sCE0MjUyRUk ''28edo blues''] (2023)
+* [https://www.youtube.com/shorts/--BIQKJ9uvI ''minuet in 28edo''] (2025)
+* [https://www.youtube.com/shorts/vEcihDrmddg ''Fantasy in 28edo''] (2026)
+; [[duckapus]]
 * [https://www.youtube.com/watch?v=F74B9qUpYi8 ''G.27 Variations in 28edo''] (2023)
 ; [[User:Eliora|Eliora]]
-* [https://www.youtube.com/watch?v=ghVCGlm7yOk ''Fantasy for Piano'']
+* [https://www.youtube.com/watch?v=ghVCGlm7yOk ''Fantasy for Piano (and strings)''] (2021)
-; Kosmorksy
+; [[Francium]]
+* [https://www.youtube.com/watch?v=8dubV7STjJA ''According to a Tomato''] (2025)
+; [[Kosmorksy]]
 * [https://www.youtube.com/watch?v=26UpCbrb3mE ''28 tone Prelude'']
-; [[Claudi Meneghin]]
+; [[User:Phanomium|Phanomium]]
+* ''[https://www.youtube.com/watch?v=zZJ5b4SkT7Q Euxenite]'' (2025)
+;[[Claudi Meneghin]]
 * [https://www.youtube.com/watch?v=30XUKJsaINU ''Happy Birthday Canon'', 5-in-1 Canon in 28edo]
+* [https://www.youtube.com/watch?v=wYdRAzp8Qi0 ''Canon on Twinkle Twinkle Little Star'', for Baroque Oboe & Viola] (2023) – ([https://www.youtube.com/watch?v=B1KZoLR8UTI for Organ])
+; [[NullPointerException Music]]
+* [https://www.youtube.com/watch?v=vw6l5b3oGk0 ''Edolian - Machinery''] (2020)
 ; [[User:Userminusone|Userminusone]]
 * [https://youtu.be/NbR3i45qQVQ ''Purple Skyes'']
-[[Category:28edo| ]] <!-- main article -->
-[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
 [[Category:Twentuning]]
+[[Category:Listen]]